TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/original-local-source-variable-background-20261102/det16-source-results.json
Original file SHA-256: 20fe3aa2b459dedaa3f6124d8f14680a08b78631ee59a130fa2e32c882ebd1f8
Inclusive original lines: 1-200
Line numbers below refer to the original source.
This bounded excerpt is source evidence; it is not a new proof/checker run.
Conversation metadata and personal execution details are omitted where indicated.

000001 | {
000002 |   "status": "pass",
000003 |   "dimension": 65536,
000004 |   "phi": 0.4487989505128276,
000005 |   "native_projector_nnz": 4,
000006 |   "hamiltonian": "2*(I-P), isolated finite mirror cluster; not full interacting cell",
000007 |   "identities_all_beta": "P\u00b2=P => exp(-beta H)=a I+b P, a=exp(-2 beta), b=1-a, Z=65536 a+b. Native finite Fock trace and rank-one P yield Cij=deltaij/2, <ci cj>=0, <ni nj>=1/4+b/(4Z) for i!=j, <Omega>=b exp(i phi)/(2Z).",
000008 |   "ordered_word_formula": "Tr[product_k ((a_k I+b_k P) O_k) (a_last I+b_last P)]/Z; expansion into 2^(number of intervals) sparse terms applies to any finite ordered CAR word, not just sampled four words.",
000009 |   "twining_scope": "Original Spin(10) center on this 16-mode Fock factor: U_q=q^N, q=1,i,-1,-i. P is invariant and Tr U_q exp(-beta H)=a(1+q)^16+b, including its zero-source offset. These are conditional Gauss weights; no full v1013 Gauss embedding is asserted.",
000010 |   "renewal_scope": "Matrix-free cyclic rank-one renewal on ambient CAR words with original Jordan-Wigner bit signs. It does not implement Gauss twining. Values below are unnormalized sparse direct traces at diagnostic beta=2*pi.",
000011 |   "renewal_comparisons": [
000012 |     {
000013 |       "name": "density4",
000014 |       "length": 4,
000015 |       "direct": [
000016 |         0.05891799270510213,
000017 |         -7.548217193685425e-21
000018 |       ],
000019 |       "renewal": [
000020 |         0.05891799270510211,
000021 |         -3.621655925796072e-20
000022 |       ],
000023 |       "absolute_error": 2.0816701452462748e-17
000024 |     },
000025 |     {
000026 |       "name": "crossed4",
000027 |       "length": 4,
000028 |       "direct": [
000029 |         0.0572964069772704,
000030 |         0.0
000031 |       ],
000032 |       "renewal": [
000033 |         0.05729640697727038,
000034 |         0.0
000035 |       ],
000036 |       "absolute_error": 2.0816681711721685e-17
000037 |     },
000038 |     {
000039 |       "name": "odd4",
000040 |       "length": 4,
000041 |       "direct": [
000042 |         0.0,
000043 |         0.0
000044 |       ],
000045 |       "renewal": [
000046 |         0.0,
000047 |         0.0
000048 |       ],
000049 |       "absolute_error": 0.0
000050 |     },
000051 |     {
000052 |       "name": "density8",
000053 |       "length": 8,
000054 |       "direct": [
000055 |         0.014788657804234148,
000056 |         -3.632939847314758e-21
000057 |       ],
000058 |       "renewal": [
000059 |         0.01478865780423415,
000060 |         -1.47880883630747e-20
000061 |       ],
000062 |       "absolute_error": 1.734759342226888e-18
000063 |     },
000064 |     {
000065 |       "name": "density16",
000066 |       "length": 16,
000067 |       "direct": [
000068 |         0.0011056026370180824,
000069 |         -7.11108238131056e-23
000070 |       ],
000071 |       "renewal": [
000072 |         0.0011056026370180824,
000073 |         -7.280877364639859e-21
000074 |       ],
000075 |       "absolute_error": 7.209766540826754e-21
000076 |     },
000077 |     {
000078 |       "name": "omega16",
000079 |       "length": 16,
000080 |       "direct": [
000081 |         2.95928108757438e-06,
000082 |         1.42511466169296e-06
000083 |       ],
000084 |       "renewal": [
000085 |         2.9592810875743725e-06,
000086 |         1.4251146616929575e-06
000087 |       ],
000088 |       "absolute_error": 8.035660099586566e-21
000089 |     },
000090 |     {
000091 |       "name": "omega_dagger16",
000092 |       "length": 16,
000093 |       "direct": [
000094 |         2.9592810875743797e-06,
000095 |         -1.42511466169296e-06
000096 |       ],
000097 |       "renewal": [
000098 |         2.9592810875743725e-06,
000099 |         -1.4251146616929575e-06
000100 |       ],
000101 |       "absolute_error": 7.635051808331911e-21
000102 |     }
000103 |   ],
000104 |   "word_validation": "4 four-operator words x 3 diagnostic beta values compared with sparse multiplication and independently expanded identity/projector terms; no dense 65536-by-65536 matrix or expm",
000105 |   "scope": "Diagnostic beta only; no physical beta calibration, full interacting v1013 cell, 4D decoupling, source derivation, Gaussian twining or full TFPT solution asserted.",
000106 |   "sources": {
000107 |     "verification/v1002_spin10_mirror_projector.py": "84f7cd7987887ee071d7e05872285ab274ae329f6bcfa693be69bb52add19a4c",
000108 |     "experiments/theory-contracts/original-local-source-variable-background-20261102/check_det16_source.py": "0511dddb7d2c1f634014e2ba7e7227aa9ed20c8aafeccb05b6bec15d9727a0a0"
000109 |   },
000110 |   "numpy": "2.5.4",
000111 |   "scipy": "1.18.1",
000112 |   "results": [
000113 |     {
000114 |       "beta": 1.0,
000115 |       "a": 0.1353352832366127,
000116 |       "b": 0.8646647167633873,
000117 |       "Z": 8870.197786911413,
000118 |       "ground_probability": 0.00011273705773230546,
000119 |       "twinedWeights": [
000120 |         {
000121 |           "center": "1",
000122 |           "zero_source_weight": [
000123 |             8870.197786911413,
000124 |             0.0
000125 |           ],
000126 |           "normalized_weight": [
000127 |             1.0,
000128 |             0.0
000129 |           ]
000130 |         },
000131 |         {
000132 |           "center": "i",
000133 |           "zero_source_weight": [
000134 |             35.51049722533624,
000135 |             0.0
000136 |           ],
000137 |           "normalized_weight": [
000138 |             0.004003348975795604,
000139 |             0.0
000140 |           ]
000141 |         },
000142 |         {
000143 |           "center": "-1",
000144 |           "zero_source_weight": [
000145 |             0.8646647167633873,
000146 |             0.0
000147 |           ],
000148 |           "normalized_weight": [
000149 |             9.747975609284154e-05,
000150 |             0.0
000151 |           ]
000152 |         },
000153 |         {
000154 |           "center": "-i",
000155 |           "zero_source_weight": [
000156 |             35.51049722533624,
000157 |             0.0
000158 |           ],
000159 |           "normalized_weight": [
000160 |             0.004003348975795604,
000161 |             0.0
000162 |           ]
000163 |         }
000164 |       ],
000165 |       "max_normal_error": 0.0,
000166 |       "max_anomalous_error": 0.0,
000167 |       "density_pair": 0.2500243699390232,
000168 |       "max_density_error": 0.0,
000169 |       "omega_expectation": [
000170 |         4.3913112745185696e-05,
000171 |         2.1147440530914827e-05
000172 |       ],
000173 |       "ordered_words": [
000174 |         {
000175 |           "name": "same mode",
000176 |           "direct": [
000177 |             0.49997823266710284,
000178 |             1.3651017903640284e-22
000179 |           ],
000180 |           "expanded": [
000181 |             0.4999782326671025,
000182 |             2.202371247246228e-23
000183 |           ],
000184 |           "absolute_error": 3.3306690738756663e-16
000185 |         },
000186 |         {
000187 |           "name": "two densities",
000188 |           "direct": [
000189 |             0.24999713965547685,
000190 |             1.3651017903640284e-22
000191 |           ],
000192 |           "expanded": [
000193 |             0.24999713965547685,
000194 |             2.202371247246228e-23
000195 |           ],
000196 |           "absolute_error": 1.1448646656394056e-22
000197 |         },
000198 |         {
000199 |           "name": "crossed",
000200 |           "direct": [